SOLUTION: Please help with this: Given the leading coefficient, a, the x coordinate of the vertex, Vx, and the y coordinate of the vertex, Vy, of quadratic function f, find the roots in ter

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Please help with this: Given the leading coefficient, a, the x coordinate of the vertex, Vx, and the y coordinate of the vertex, Vy, of quadratic function f, find the roots in ter      Log On


   

Question 916939: Please help with this:
Given the leading coefficient, a, the x coordinate of the vertex, Vx, and the y coordinate of the vertex, Vy, of quadratic function f, find the roots in terms of a, Vx, and Vy.
Thank You for taking the time to look at this!
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
This is mostly just symbolic substitution and then simple algebraic steps.

Put the function into standard form using your given information.

highlight_green%28f%28x%29=a%28x-Vx%29%5E2%2BVy%29, and as you, I am continuing to assume the lower case character in the mixed notation is like a subscript.

Wanting the roots, just equate f(x) to 0.
a%28x-Vx%29%5E2%2BVy=0
Solve for "x".

a%28x-Vx%29%5E2=-Vy
%28x-Vx%29%5E2=-%281%2Fa%29Vy
.
x=Vx%2B-+sqrt%28-Vy%2Fa%29
.
x=Vx%2B-+%281%2Fa%29sqrt%28-Vy%2Aa%29

You really want to make sure your subscripts "look like" subscripts and not simply extra attached variables; so you really should show...
highlight%28x=V%5Bx%5D%2B-+%281%2Fa%29sqrt%28-V%5By%5D%2Aa%29%29